'Win or Lose?' printed from http://nrich.maths.org/

A gambler bets half the money in his pocket on the toss of a coin, winning an equal amount for a head and losing his money if the result is a tail. He repeats this many times, each time betting half the total money he has. After $2n$ plays he has won exactly $n$ times. Has he more money, the same amount or less money than he started with?